Question

Simplify:12^3×15^4/81×25^2

Answer 1

To simplify the given expression, apply the rules of exponents and cancel out the bases and exponents to get the final result as 1.

Step-by-step explanation:

To simplify the given expression, we need to apply the rules of exponents:

1. Use the power of a power rule to simplify the bases.
2. Apply the power of a product rule to simplify the exponents.
3. Combine the simplified terms.

Following these steps, we get:
123 × 154 / 81 × 252 = (12 × 152)2 / (34 × 54) × 252

Now, simplify the bases and exponents. Note that 152 = (3 × 5)2, 34 = (32)2, and 54 = (52)2.

After simplifying, we have:
(12 × 32 × 52)2 / (32 × 52)2 × 252

Since the bases and exponents are the same in the numerator and denominator, they cancel out, leaving us with:
1 / 1 × 1 = 1

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